On q-Difference Riccati Equations and Second-Order Linear q-Difference Equations. (13th January 2013) - Huang, Zhi-Bo
Abstract : We consider q -difference Riccati equations and second-order linear q -difference equations in the complex plane. We present some basic properties, such as the transformations between these two equations, the representations and the value distribution of meromorphic solutions of q -difference Riccati equations, and the q -Casorati determinant of meromorphic solutions of second-order linear q -difference equations. In particular, we find that the meromorphic solutions of these two equations are concerned with the q -Gamma function when q ∈ ℂ such that 0 < | q | < 1 . Some examples are also listed to illustrate our results.